C₂×#10930 #354081

order	512
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

C₂×#10930

Subgroups

	subgroup	G/H
center	C₂³×C₄	C₂×D₄
commutator	C₂×C₄	C₂²×C₄²
Frattini, cosocle	C₂³×C₄	C₂⁴
socle	C₂⁴	C₄×D₄
prime radical	C₂³×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁴×C₈ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

3034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4)(5,6)(8,10)(11,12,16,19,15,20,14,17)(13,21,24,25,22,18,23,26);(4,6)(12,17,20,19)(13,22)(18,26,21,25)(23,24);(7,8,9,10)(11,13,14,23,15,22,16,24)(12,18,17,25,20,21,19,26)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#354635, #72215962, #72215970, …
maximal normal subgroup of	C₂×#354635, #72215962, #72215970, …
maximal quotient of	C₂×#110276, #72321576, #72323122

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261277);

C2×#10930 #354081

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×#10930 #354081